Answer: The correct option is (B) \(\dfrac{1}{2}(n+2)-\dfrac{2}{5}n=5.\)
Step-by-step explanation: We are given to select the correct equation to determine two consecutive even numbers such that the difference of one-half the larger and two-fifths the smaller is equal to five.
Let, 'n' and '(n + 2)' be the two consecutive even numbers.
Then, according to the given information, the equation can be written as
\(\dfrac{1}{2}\times (n+2)-\dfrac{2}{5}\times n=5\\\\\\\Rightarrow \dfrac{1}{2}(n+2)-\dfrac{2}{5}n=5\\\\\\\Rightarrow \dfrac{5(n+2)-4n}{10}=5\\\\\Rightarrow 5n+10-4n=50\\\\\Rightarrow n=50-10\\\\\Rightarrow n=40.\)
So, n = 40 and n + 2 = 40 + 2 = 42.
Thus, the two even numbers are 40 and 42.
And, the required equation is \(\dfrac{1}{2}(n+2)-\dfrac{2}{5}n=5.\)
Option (B) is correct.
